1029/1000: Difference between revisions
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'''1029/1000''', the '''keega''', is a [[medium comma|medium]] [[7-limit]] [[comma]] measuring about 49.5 [[cent]]s. It is the difference between a stack of three [[10/7]]'s and a perfect twelfth ([[3/1]]), or between a stack of three [[7/5]]'s and a perfect eleventh ([[8/3]]), and arises from [[10/7]] being a convergent in the continued fraction of <math>\sqrt[3]{3}</math>. | |||
It factors into simpler commas as ([[49/48]])⋅([[126/125]]) and ([[81/80]])⋅([[686/675]]). | |||
== Temperaments == | == Temperaments == | ||
Tempering out this comma in the 7-limit leads to the rank-3 [[keegic]] temperament. See [[ | [[Tempering out]] this comma in the 7-limit leads to the rank-3 [[keegic]] temperament. See [[Keegic temperaments]] for a collection of rank-2 temperaments where it is tempered out. | ||
== Etymology == | == Etymology == | ||
The name ''keega'' was given by [[Gene Ward Smith]] in 2005. It is a contraction of ''[[keemun]]'' and ''gawel'', although ''gawel'' was later renamed to ''[[liese]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group | ''Seven limit comma names from pairs of temperament names'']</ref>. | The name ''keega'' was given by [[Gene Ward Smith]] in 2005. It is a contraction of ''[[keemun]]'' and ''gawel'', although ''gawel'' was later renamed to ''[[liese]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group | ''Seven limit comma names from pairs of temperament names'']</ref>. | ||
== | == References == | ||
[[Category:Keegic]] | [[Category:Keegic]] | ||
[[Category:Commas named by combining multiple temperament names]] | |||
Latest revision as of 12:12, 21 January 2026
| Interval information |
1029/1000, the keega, is a medium 7-limit comma measuring about 49.5 cents. It is the difference between a stack of three 10/7's and a perfect twelfth (3/1), or between a stack of three 7/5's and a perfect eleventh (8/3), and arises from 10/7 being a convergent in the continued fraction of [math]\displaystyle{ \sqrt[3]{3} }[/math].
It factors into simpler commas as (49/48)⋅(126/125) and (81/80)⋅(686/675).
Temperaments
Tempering out this comma in the 7-limit leads to the rank-3 keegic temperament. See Keegic temperaments for a collection of rank-2 temperaments where it is tempered out.
Etymology
The name keega was given by Gene Ward Smith in 2005. It is a contraction of keemun and gawel, although gawel was later renamed to liese[1].